%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SWC396+1 : TPTP v9.2.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n022.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 5 05:19:29 PM UTC 2026
% Result : Theorem 1.61s 1.86s
% Output : CNFRefutation 1.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 15
% Syntax : Number of formulae : 85 ( 16 unt; 0 def)
% Number of atoms : 389 ( 125 equ)
% Maximal formula atoms : 25 ( 4 avg)
% Number of connectives : 493 ( 189 ~; 211 |; 48 &)
% ( 5 <=>; 40 =>; 0 <=; 0 <~>)
% Maximal formula depth : 30 ( 6 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 6 con; 0-2 aty)
% Number of variables : 115 ( 0 sgn 65 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1,conjecture,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ! [X5] :
( ssItem(X5)
=> ( ~ memberP(X1,X5)
| memberP(X2,X5) ) )
| ( nil != X3
& nil = X4 )
| ( neq(X4,nil)
& ( ~ neq(X3,nil)
| ? [X6] :
( ssList(X6)
& X4 != X6
& ? [X7] :
( ssList(X7)
& ? [X8] :
( ssList(X8)
& tl(X3) = X7
& app(X7,X8) = X6
& ? [X9] :
( ssItem(X9)
& cons(X9,nil) = X8
& hd(X3) = X9
& neq(nil,X3) )
& neq(nil,X3) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).
fof(ax26,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ssList(app(X1,X2)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax26) ).
fof(ax24,axiom,
! [X1] :
( ssList(X1)
=> ( nil != X1
=> ssList(tl(X1)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax24) ).
fof(ax16,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> ssList(cons(X2,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax16) ).
fof(ax17,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax17) ).
fof(ax22,axiom,
! [X1] :
( ssList(X1)
=> ( nil != X1
=> ssItem(hd(X1)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax22) ).
fof(ax15,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( neq(X1,X2)
<=> X1 != X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax15) ).
fof(ax78,axiom,
! [X1] :
( ssList(X1)
=> ( nil != X1
=> cons(hd(X1),tl(X1)) = X1 ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax78) ).
fof(ax86,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( nil != X1
=> tl(app(X1,X2)) = app(tl(X1),X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax86) ).
fof(ax83,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( nil = app(X1,X2)
<=> ( nil = X2
& nil = X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax83) ).
fof(ax85,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( nil != X1
=> hd(app(X1,X2)) = hd(X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax85) ).
fof(ax36,axiom,
! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( memberP(app(X2,X3),X1)
<=> ( memberP(X2,X1)
| memberP(X3,X1) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax36) ).
fof(ax3,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> ( memberP(X1,X2)
<=> ? [X3] :
( ssList(X3)
& ? [X4] :
( ssList(X4)
& app(X3,cons(X2,X4)) = X1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax3) ).
fof(ax37,axiom,
! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssItem(X2)
=> ! [X3] :
( ssList(X3)
=> ( memberP(cons(X2,X3),X1)
<=> ( X1 = X2
| memberP(X3,X1) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax37) ).
fof(ax38,axiom,
! [X1] :
( ssItem(X1)
=> ~ memberP(nil,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax38) ).
fof(c_0_15,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ! [X5] :
( ssItem(X5)
=> ( ~ memberP(X1,X5)
| memberP(X2,X5) ) )
| ( nil != X3
& nil = X4 )
| ( neq(X4,nil)
& ( ~ neq(X3,nil)
| ? [X6] :
( ssList(X6)
& X4 != X6
& ? [X7] :
( ssList(X7)
& ? [X8] :
( ssList(X8)
& tl(X3) = X7
& app(X7,X8) = X6
& ? [X9] :
( ssItem(X9)
& cons(X9,nil) = X8
& hd(X3) = X9
& neq(nil,X3) )
& neq(nil,X3) ) ) ) ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[co1])]) ).
fof(c_0_16,negated_conjecture,
! [X471,X472,X473,X474] :
( ssList(esk48_0)
& ssList(esk49_0)
& ssList(esk50_0)
& ssList(esk51_0)
& esk49_0 = esk51_0
& esk48_0 = esk50_0
& ssItem(esk52_0)
& memberP(esk48_0,esk52_0)
& ~ memberP(esk49_0,esk52_0)
& ( nil = esk50_0
| nil != esk51_0 )
& ( neq(esk50_0,nil)
| ~ neq(esk51_0,nil) )
& ( ~ ssList(X471)
| esk51_0 = X471
| ~ ssList(X472)
| ~ ssList(X473)
| tl(esk50_0) != X472
| app(X472,X473) != X471
| ~ ssItem(X474)
| cons(X474,nil) != X473
| hd(esk50_0) != X474
| ~ neq(nil,esk50_0)
| ~ neq(nil,esk50_0)
| ~ neq(esk51_0,nil) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_15])])])])]) ).
cnf(c_0_17,negated_conjecture,
( esk51_0 = X1
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| tl(esk50_0) != X2
| app(X2,X3) != X1
| ~ ssItem(X4)
| cons(X4,nil) != X3
| hd(esk50_0) != X4
| ~ neq(nil,esk50_0)
| ~ neq(nil,esk50_0)
| ~ neq(esk51_0,nil) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
fof(c_0_18,plain,
! [X345,X346] :
( ~ ssList(X345)
| ~ ssList(X346)
| ssList(app(X345,X346)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax26])])]) ).
cnf(c_0_19,negated_conjecture,
( esk51_0 = X1
| hd(esk50_0) != X4
| tl(esk50_0) != X2
| app(X2,X3) != X1
| cons(X4,nil) != X3
| ~ ssItem(X4)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ neq(nil,esk50_0)
| ~ neq(esk51_0,nil) ),
inference(cn,[status(thm)],[c_0_17]) ).
cnf(c_0_20,plain,
( ssList(app(X1,X2))
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
fof(c_0_21,plain,
! [X342] :
( ~ ssList(X342)
| nil = X342
| ssList(tl(X342)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax24])]) ).
cnf(c_0_22,negated_conjecture,
ssList(esk48_0),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_23,negated_conjecture,
esk48_0 = esk50_0,
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_24,negated_conjecture,
( app(tl(esk50_0),cons(hd(esk50_0),nil)) = esk51_0
| ~ ssList(cons(hd(esk50_0),nil))
| ~ ssList(tl(esk50_0))
| ~ neq(nil,esk50_0)
| ~ neq(esk51_0,nil)
| ~ ssItem(hd(esk50_0)) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_19])])])]),c_0_20]) ).
cnf(c_0_25,plain,
( nil = X1
| ssList(tl(X1))
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_26,negated_conjecture,
ssList(esk50_0),
inference(rw,[status(thm)],[c_0_22,c_0_23]) ).
fof(c_0_27,plain,
! [X326,X327] :
( ~ ssList(X326)
| ~ ssItem(X327)
| ssList(cons(X327,X326)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax16])])]) ).
cnf(c_0_28,negated_conjecture,
( app(tl(esk50_0),cons(hd(esk50_0),nil)) = esk51_0
| esk50_0 = nil
| ~ ssList(cons(hd(esk50_0),nil))
| ~ neq(nil,esk50_0)
| ~ neq(esk51_0,nil)
| ~ ssItem(hd(esk50_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26])]) ).
cnf(c_0_29,plain,
( ssList(cons(X2,X1))
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_30,plain,
ssList(nil),
inference(split_conjunct,[status(thm)],[ax17]) ).
fof(c_0_31,plain,
! [X339] :
( ~ ssList(X339)
| nil = X339
| ssItem(hd(X339)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax22])]) ).
cnf(c_0_32,negated_conjecture,
( app(tl(esk50_0),cons(hd(esk50_0),nil)) = esk51_0
| esk50_0 = nil
| ~ neq(nil,esk50_0)
| ~ neq(esk51_0,nil)
| ~ ssItem(hd(esk50_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_30])]) ).
cnf(c_0_33,plain,
( nil = X1
| ssItem(hd(X1))
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
fof(c_0_34,plain,
! [X324,X325] :
( ( ~ neq(X324,X325)
| X324 != X325
| ~ ssList(X325)
| ~ ssList(X324) )
& ( X324 = X325
| neq(X324,X325)
| ~ ssList(X325)
| ~ ssList(X324) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax15])])])]) ).
fof(c_0_35,plain,
! [X428] :
( ~ ssList(X428)
| nil = X428
| cons(hd(X428),tl(X428)) = X428 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax78])]) ).
fof(c_0_36,plain,
! [X445,X446] :
( ~ ssList(X445)
| ~ ssList(X446)
| nil = X445
| tl(app(X445,X446)) = app(tl(X445),X446) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax86])])]) ).
fof(c_0_37,plain,
! [X440,X441] :
( ( nil = X441
| nil != app(X440,X441)
| ~ ssList(X441)
| ~ ssList(X440) )
& ( nil = X440
| nil != app(X440,X441)
| ~ ssList(X441)
| ~ ssList(X440) )
& ( nil != X441
| nil != X440
| nil = app(X440,X441)
| ~ ssList(X441)
| ~ ssList(X440) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax83])])])]) ).
cnf(c_0_38,negated_conjecture,
( app(tl(esk50_0),cons(hd(esk50_0),nil)) = esk51_0
| esk50_0 = nil
| ~ neq(nil,esk50_0)
| ~ neq(esk51_0,nil) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_26])]) ).
cnf(c_0_39,plain,
( X1 = X2
| neq(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_40,negated_conjecture,
ssList(esk49_0),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_41,negated_conjecture,
esk49_0 = esk51_0,
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_42,plain,
( nil = X1
| cons(hd(X1),tl(X1)) = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_43,plain,
( nil = X1
| tl(app(X1,X2)) = app(tl(X1),X2)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_44,plain,
( nil = X1
| nil != app(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_45,negated_conjecture,
( app(tl(esk50_0),cons(hd(esk50_0),nil)) = esk51_0
| esk50_0 = nil
| ~ neq(esk51_0,nil) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_26]),c_0_30])]) ).
cnf(c_0_46,negated_conjecture,
ssList(esk51_0),
inference(rw,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_47,negated_conjecture,
( nil = esk50_0
| nil != esk51_0 ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_48,plain,
( cons(hd(app(X1,X2)),app(tl(X1),X2)) = app(X1,X2)
| nil = X1
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_20]),c_0_44]) ).
cnf(c_0_49,negated_conjecture,
( app(tl(esk50_0),cons(hd(esk50_0),nil)) = esk51_0
| esk50_0 = nil ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_39]),c_0_30]),c_0_46])]),c_0_47]) ).
cnf(c_0_50,negated_conjecture,
( cons(hd(app(esk50_0,cons(hd(esk50_0),nil))),esk51_0) = app(esk50_0,cons(hd(esk50_0),nil))
| esk50_0 = nil
| ~ ssList(cons(hd(esk50_0),nil)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_49]),c_0_26])]) ).
cnf(c_0_51,negated_conjecture,
( cons(hd(app(esk50_0,cons(hd(esk50_0),nil))),esk51_0) = app(esk50_0,cons(hd(esk50_0),nil))
| esk50_0 = nil
| ~ ssItem(hd(esk50_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_29]),c_0_30])]) ).
fof(c_0_52,plain,
! [X443,X444] :
( ~ ssList(X443)
| ~ ssList(X444)
| nil = X443
| hd(app(X443,X444)) = hd(X443) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax85])])]) ).
cnf(c_0_53,negated_conjecture,
( cons(hd(app(esk50_0,cons(hd(esk50_0),nil))),esk51_0) = app(esk50_0,cons(hd(esk50_0),nil))
| esk50_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_33]),c_0_26])]) ).
cnf(c_0_54,plain,
( nil = X1
| hd(app(X1,X2)) = hd(X1)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[c_0_52]) ).
fof(c_0_55,plain,
! [X366,X367,X368] :
( ( ~ memberP(app(X367,X368),X366)
| memberP(X367,X366)
| memberP(X368,X366)
| ~ ssList(X368)
| ~ ssList(X367)
| ~ ssItem(X366) )
& ( ~ memberP(X367,X366)
| memberP(app(X367,X368),X366)
| ~ ssList(X368)
| ~ ssList(X367)
| ~ ssItem(X366) )
& ( ~ memberP(X368,X366)
| memberP(app(X367,X368),X366)
| ~ ssList(X368)
| ~ ssList(X367)
| ~ ssItem(X366) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax36])])])]) ).
cnf(c_0_56,negated_conjecture,
memberP(esk48_0,esk52_0),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_57,negated_conjecture,
( app(esk50_0,cons(hd(esk50_0),nil)) = cons(hd(esk50_0),esk51_0)
| esk50_0 = nil
| ~ ssList(cons(hd(esk50_0),nil)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_54]),c_0_26])]) ).
cnf(c_0_58,plain,
( memberP(app(X1,X3),X2)
| ~ memberP(X1,X2)
| ~ ssList(X3)
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[c_0_55]) ).
cnf(c_0_59,negated_conjecture,
memberP(esk50_0,esk52_0),
inference(rw,[status(thm)],[c_0_56,c_0_23]) ).
cnf(c_0_60,negated_conjecture,
ssItem(esk52_0),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_61,negated_conjecture,
( app(esk50_0,cons(hd(esk50_0),nil)) = cons(hd(esk50_0),esk51_0)
| esk50_0 = nil
| ~ ssItem(hd(esk50_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_29]),c_0_30])]) ).
fof(c_0_62,plain,
! [X226,X227,X230,X231] :
( ( ssList(esk3_2(X226,X227))
| ~ memberP(X226,X227)
| ~ ssItem(X227)
| ~ ssList(X226) )
& ( ssList(esk4_2(X226,X227))
| ~ memberP(X226,X227)
| ~ ssItem(X227)
| ~ ssList(X226) )
& ( app(esk3_2(X226,X227),cons(X227,esk4_2(X226,X227))) = X226
| ~ memberP(X226,X227)
| ~ ssItem(X227)
| ~ ssList(X226) )
& ( ~ ssList(X230)
| ~ ssList(X231)
| app(X230,cons(X227,X231)) != X226
| memberP(X226,X227)
| ~ ssItem(X227)
| ~ ssList(X226) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax3])])])])]) ).
cnf(c_0_63,negated_conjecture,
( memberP(app(esk50_0,X1),esk52_0)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_59]),c_0_26]),c_0_60])]) ).
cnf(c_0_64,negated_conjecture,
( app(esk50_0,cons(hd(esk50_0),nil)) = cons(hd(esk50_0),esk51_0)
| esk50_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_33]),c_0_26])]) ).
cnf(c_0_65,plain,
( memberP(X4,X3)
| ~ ssList(X1)
| ~ ssList(X2)
| app(X1,cons(X3,X2)) != X4
| ~ ssItem(X3)
| ~ ssList(X4) ),
inference(split_conjunct,[status(thm)],[c_0_62]) ).
cnf(c_0_66,negated_conjecture,
( esk50_0 = nil
| memberP(cons(hd(esk50_0),esk51_0),esk52_0)
| ~ ssList(cons(hd(esk50_0),nil)) ),
inference(spm,[status(thm)],[c_0_63,c_0_64]) ).
cnf(c_0_67,plain,
( memberP(app(X1,cons(X2,X3)),X2)
| ~ ssList(app(X1,cons(X2,X3)))
| ~ ssList(X3)
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(er,[status(thm)],[c_0_65]) ).
fof(c_0_68,plain,
! [X369,X370,X371] :
( ( ~ memberP(cons(X370,X371),X369)
| X369 = X370
| memberP(X371,X369)
| ~ ssList(X371)
| ~ ssItem(X370)
| ~ ssItem(X369) )
& ( X369 != X370
| memberP(cons(X370,X371),X369)
| ~ ssList(X371)
| ~ ssItem(X370)
| ~ ssItem(X369) )
& ( ~ memberP(X371,X369)
| memberP(cons(X370,X371),X369)
| ~ ssList(X371)
| ~ ssItem(X370)
| ~ ssItem(X369) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax37])])])]) ).
cnf(c_0_69,negated_conjecture,
( esk50_0 = nil
| memberP(cons(hd(esk50_0),esk51_0),esk52_0)
| ~ ssItem(hd(esk50_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_29]),c_0_30])]) ).
cnf(c_0_70,negated_conjecture,
~ memberP(esk49_0,esk52_0),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_71,negated_conjecture,
( esk50_0 = nil
| memberP(esk51_0,hd(esk50_0))
| ~ ssList(tl(esk50_0))
| ~ ssItem(hd(esk50_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_49]),c_0_46]),c_0_30])]) ).
cnf(c_0_72,plain,
( X3 = X1
| memberP(X2,X3)
| ~ memberP(cons(X1,X2),X3)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X3) ),
inference(split_conjunct,[status(thm)],[c_0_68]) ).
cnf(c_0_73,negated_conjecture,
( esk50_0 = nil
| memberP(cons(hd(esk50_0),esk51_0),esk52_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_33]),c_0_26])]) ).
cnf(c_0_74,negated_conjecture,
~ memberP(esk51_0,esk52_0),
inference(rw,[status(thm)],[c_0_70,c_0_41]) ).
cnf(c_0_75,negated_conjecture,
( esk50_0 = nil
| memberP(esk51_0,hd(esk50_0))
| ~ ssItem(hd(esk50_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_25]),c_0_26])]) ).
cnf(c_0_76,negated_conjecture,
( hd(esk50_0) = esk52_0
| esk50_0 = nil
| ~ ssItem(hd(esk50_0)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_73]),c_0_46]),c_0_60])]),c_0_74]) ).
fof(c_0_77,plain,
! [X1] :
( ssItem(X1)
=> ~ memberP(nil,X1) ),
inference(fof_simplification,[status(thm)],[ax38]) ).
cnf(c_0_78,negated_conjecture,
( esk50_0 = nil
| memberP(esk51_0,hd(esk50_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_33]),c_0_26])]) ).
cnf(c_0_79,negated_conjecture,
( hd(esk50_0) = esk52_0
| esk50_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_33]),c_0_26])]) ).
fof(c_0_80,plain,
! [X372] :
( ~ ssItem(X372)
| ~ memberP(nil,X372) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_77])]) ).
cnf(c_0_81,negated_conjecture,
esk50_0 = nil,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_79]),c_0_74]) ).
cnf(c_0_82,plain,
( ~ ssItem(X1)
| ~ memberP(nil,X1) ),
inference(split_conjunct,[status(thm)],[c_0_80]) ).
cnf(c_0_83,negated_conjecture,
memberP(nil,esk52_0),
inference(rw,[status(thm)],[c_0_59,c_0_81]) ).
cnf(c_0_84,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_83]),c_0_60])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWC396+1 : TPTP v9.2.1. Released v2.4.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.16/0.33 % Computer : n022.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue May 5 04:48:06 EDT 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.35 % start to proof: theBenchmark
% 1.61/1.86 % Version : CSE_E---1.7
% 1.61/1.86 % Problem : theBenchmark.p
% 1.61/1.86 % SZS status Theorem for theBenchmark.p
% 1.61/1.86 % SZS output start CNFRefutation
% See solution above
% 1.61/1.86 % Total time : 1.418s
%------------------------------------------------------------------------------